Mar 21, 2007


After three weeks fighting against an horde of evil bacteria which were trying to eat me alive, I finally have some time to write. It looks a little exaggerated, but apart from the word 'evil' and the fact that it may well be a virus, the rest is true.

Okay, back to physics. While I was in home these days I was studying a little of Loop Quantum Gravity. LQG is also called Canonical Quantum Gravity because the idea is to try to quantize gravity without using perturbative methods by a technique called canonical quantization. Now, instead of talking about what is canonical quantization, I would like to go through another path. I would like to talk about the more general procedure named 'quantization'. I decided to write about it because in one of the papers I was reading the author wrote that LQG was based in a well understood quantization procedure. I do not deny that canonical quantization is a well understood method to transform a classical theory in a quantum one mathematically, but this rang a bell in my head because, in the end, the whole thing of 'quantizing' is, in reality, far from being well understood conceptually. Let me explain better.

Quantum Mechanics is believed to be the true fundamental theory of nature. There is little doubt about that given the overwhelming experimental evidence in favor of it. So, the aim is to make all known theories compatible with QM. But nobody really knows what is the real principles of QM. Yes, this is the truth. However, using a lot of analogies, genial insights and mathematical efforts, we were able to make 3 of the 4 forces known in nature compatible with what we know is true in QM. Nowadays, after more than a century of QM, it seems that we are on our way to quantize the last one, namely gravity, using again mathematical analogies. These mathematical analogies are called quantization methods, but they are exactly that: mathematical techniques. We substitute real variables by hermitian operators, real Poisson brackets by commutators, expand the solution of the equations in Fourier series and define creation and annihilation operators but, what is really going on here, nobody truly knows.

The problem is that is quite embarassing for a theory that should be the fundamental one when we have to derive its equations first from the not-so-correct one and then quantizing (modifying following some recipe) it. Conceptually, it would be desirable to start with some quantum mechanical principles, derive the QM equations and, through some limit, recover the classical results. This would be the ideal, but it seems that we are far away from this goal. And maybe that is the reason why gravity is so difficult to quantize and why there are those incovenient infinities in quantum field theory. Probably, when we find the true quantum principles, we will discover that all the quantization methods are thumb rules to go from one limit to another. This is a difficult endeavour and maybe the solution would just appear when we discover new phenomena or maybe when someone have a strikingly new idea. I will risk to say that this would be still even more exciting than even quantizing gravity, for it would change (again) completely our view of nature.

I'll be optimist and hope that I can see it still in my lifetime. There are quite a lot of clever people working on these matters today. There are the Bayesian approaches, the more or less old Bohmian Mechanics, Nelson's QM and a lot of other tentatives, but something is still lacking. I believe that when the answer comes it will be like when you learn relativity: "Why did nobody think about it before? It's so obvious!" I mean, it is that feeling that every piece has fitted together. Well, I'll wait. :)

Picture: Taken from the University of Tokyo's Website.

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